Since it doesn't have a destruction effect on it I think it stays in play until removed by something.
For Scholar, I'd say to attack La Capitan, I'll be dealing a good bit of damage to L'Epeiste on my turn.
Which I'll take now:
Sky-scraper lost Catch a Ride to La Capitan, but it is now in her deck.
Returned Undectable Relinking to the top of my deck.
Sky-Scraper
Tiny
HP: 9
Hand: Rest and Recover, Explosive Reveal, Micro-Assembler, Aggresion Modulator, Thorathian Monolith, Compulsion Cannister, Tectonic Chokeslam, Thorathian Monolith, Compulsion Cannister
In Play: Proportionist, Cortext Hyperstimulator (La Capitan), Neutralizing Resonator (La Capitan), Aggresion Modulator (Next to Nothing,) Rebounding Debilitator (La Capitan), Micro Assembler (Tempest,) Cortex HyperStimulaor (La Capitan)
Discard: Rebounding Debilitator, Colossal Left Hook, Tectonic Chokeslam, Catch a Ride, Linking Incursion, Undectable Relinking, Undectable Relinking
Under La Capitan: None
Effects:
-Tempest has Power: Discard a card, then search your deck for an equipment card and put it either into your hand or into play, then shuffle your deck
-When La Capitan would deal 3 or more damage prevent that damage and Rebounding Debilitator goes to the top of Sky-scraper's deck or is discarded.
-At the start of Sky-Scrapers she may destory one Ongoing Card, if she does destroy Neutralizing Resonator.
-Reduce the first damage dealt each turn by La Capitan by two
-At the end of the Villain turn La Capitan deals herself 1 lighting damage
-At the end of the Villain turn La Capitan deals herself 1 lightning damage
-Increase Sonic Damage dealt by Sky-Scraper by 1
-When Sky-Scraper switches to a larger size deal each non-villain target 1 melee damage
-When Sky-Scraper switches to a smaller size, draw a card
------Turn-----
(I'm assuming Scholar picks La Capitan for his 2 damage, and I believie only 1 damage has been done to L'Epeiste, so I'm figuring from HP [62] and [6] respectively, let me know if I'm wrong.)
Play: Rest and Recover
-Sky-Scraper switches to larger size (Normal) so she deals 1 damage to all non-hero targets, La Capitan [61], L'Epeiste [5]
-Sky-Scraper regains 1 HP [12], draws one card (Undectable Relinking,) and returns Colossal Left Hook to her hand
Play: Colossal Left Hook
Sky-Scraper switches to larger size (Huge) so she deals 1 damage to all non-ero targets, La Capitan [60] and L'Epeiste [4.]
-She deals La Capitan 3 damage [57] and discards Micro-Assembler to play another card.
Play: Tectonic Chokeslam
-Sky-Scraper deals La Capitan 4 damage [53,] Sky-scraper deals ever target 1 projectile damage:
La Capitan [52], L'Epeiste [3]
She will hit Dynamic Syphon to allow a power use for Tempest (but don't using Cleansing Downpour yet, because:)
Power: Concussive Clap
Sky-Scraper delas each non-hero target 2[+1] damage (La Captian [49] L'Epeiste [x])
Sky-Scraper deals each hero target 0[+1] damage, hitting Dynamic Syphon again, which I think means everybody is back where they were at (except Tempest who soaked the damage and is now at [15]
Draw: Linking Incursion
Draw: Explosive Reveal
----End of Turn----
Sky-Scraper
Huge
HP: 10
Hand: Explosive Reveal, Explosive Reveal, Aggresion Modulator, Thorathian Monolith, Compulsion Cannister, Thorathian Monolith, Compulsion Cannister, Linking Incursion, Undectable Relinking
In Play: Proportionist, Cortext Hyperstimulator (La Capitan), Neutralizing Resonator (La Capitan), Aggresion Modulator (Next to Nothing,) Rebounding Debilitator (La Capitan), Micro Assembler (Tempest,) Cortex HyperStimulaor (La Capitan)
Discard: Rebounding Debilitator, Colossal Left Hook, Tectonic Chokeslam, Catch a Ride, Linking Incursion, Undectable Relinking, Undectable Relinking
Under La Capitan: None
Effects:
-Tempest has Power: Discard a card, then search your deck for an equipment card and put it either into your hand or into play, then shuffle your deck
-When La Capitan would deal 3 or more damage prevent that damage and Rebounding Debilitator goes to the top of Sky-scraper's deck or is discarded.
-At the start of Sky-Scrapers she may destory one Ongoing Card, if she does destroy Neutralizing Resonator.
-Reduce the first damage dealt each turn by La Capitan by two
-At the end of the Villain turn La Capitan deals herself 1 lighting damage
-At the end of the Villain turn La Capitan deals herself 1 lightning damage
-Increase Sonic Damage dealt by Sky-Scraper by 1
-When Sky-Scraper switches to a larger size deal each non-villain target 1 melee damage
-When Sky-Scraper switches to a smaller size, draw a card
Notes: I think this is the best way to play my turn, I can also play it in such a way that I am Tiny, deal La'Capitan one more damage, but don't give Tempest the power uses, which I can change to if we think that's better.
-Tempest has two power uses.